What is (\partial)/(\partial x)((z)(z^3-3xyz)) ?

The answer to (\partial)/(\partial x)((z)(z^3-3xyz)) is -3z^2y

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(\partial)/(\partial x)((z)(z^3-3xyz))

\frac{\partial}{\partial x} ((z) (z^{3} - 3 x yz))

- 3 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (z^{3} - 3 x yz))

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (z^{3} - 3 x yz)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial x} (z^{3}) - \frac{\partial}{\partial x} (3 x yz))

\frac{\partial}{\partial x} (z^{3}) = 0

\frac{\partial}{\partial x} (3 x yz) = 3 zy

= z (0 - 3 zy)

Simplify

z (0 - 3 zy) : - 3 z^{2} y

= - 3 z^{2} y

\frac{1}{( x + 2 ) ( x + 1 )}

(1 - x^{2}) p^{''} (x) - 2 x p^{'} (x)

3 (e - 1)

\frac{( k - 1 ) x ^{2} + k x + 1}{( x + 3 )}

- 3 (x + y t) e^{- 3 t} + 2 (y) e^{- 3 t}

What is (\partial)/(\partial x)((z)(z^3-3xyz)) ?
The answer to (\partial)/(\partial x)((z)(z^3-3xyz)) is -3z^2y